Analysis of Dynamic Systems With Various Friction Laws

[+] Author and Article Information
J. Awrejcewicz

Department of Automatics and Biomechanics,  Technical University of Lodz, Lodz, Polandawrejcew@p.lodz.pl

P. Olejnik

Department of Automatics and Biomechanics,  Technical University of Lodz, Lodz, Polandolejnikp@p.lodz.pl

Appl. Mech. Rev 58(6), 389-411 (Nov 01, 2005) (23 pages) doi:10.1115/1.2048687 History:

This survey is devoted to the significant role of various dry friction laws in engineering sciences. Both advantages and disadvantages of a frictional process are illustrated and discussed, but excluding the nature of friction. It is shown how the classical friction laws and modern friction theories exist in today’s pure and applied sciences. Static and dynamic friction models are described. An important role of purely theoretical and experimental investigations in developing the appropriate friction models is outlined, placing an emphasis on new approaches (models proposed by Bay-Wanheim, Dahl, Bliman-Sorine, Lund-Grenoble, as well as atomic scale and fractal models, among others). Friction treated as a complex process being in interaction with wear, heat emission, and deformation is also discussed. Then the impact of dry friction models on current dynamical systems theory is reviewed. Finally, an application of friction to model a brake mechanism as a mechanical system with two degrees-of-freedom, including experimental and numerical analyses, is given. This review paper contains 254 references.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 14

Dynamic friction model

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Figure 15

Basic energy flow in systems with friction

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Figure 16

Theoretical 2-DOF model of a brake mechanism

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Figure 17

Model of a brake mechanism with intensified braking force

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Figure 18

A scheme of the Girling duo-servobrake mechanism

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Figure 19

Girling duo-servo brake: 1-hydraulic servo, 2-brake blocks with linings, 3-coupling element (see Fig. 1), 4-long return spring that pulls the brake blocks back, 5-short return spring, 6-hand-brake mechanism, 7-drum

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Figure 20

The laboratory rig

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Figure 1

Friction characteristics: (a) Coulomb law and (b) the exponential law

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Figure 2

Approximate Burridge-Knopoff model

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Figure 3

Friction characteristics for the Burridge-Knopoff model

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Figure 4

Exponential law of friction versus relative velocity

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Figure 5

Mechanical model of a passive vibrations absorber

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Figure 6

Friction models: (a) Coulomb, (b) of a falling characteristics and (c) for Fs>Fk

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Figure 7

General form of a dry friction model (F-friction force, vr-relative velocity, Fs-friction force at the moment of breaking, vmax-maximum relative velocity)

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Figure 8

Friction characteristic for periodically excited oscillator

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Figure 9

Fractal friction model for an unilateral contact

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Figure 10

A decaying characteristic of dry friction for ith constraint

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Figure 11

Oscillator on an inclined plane

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Figure 12

Friction force F as a function dependent on sliding velocity vr

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Figure 13

Relation between pressure and deformation

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Figure 21

Friction force characteristics for positive (F+) and negative (F−) relative velocity

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Figure 22

Bifurcation diagram of α1∊(2.72;4.32) parameter versus x1 displacement in the time interval from τ0=1000 to τk=51000 [α1=3,α2=1.159,η1,2,12=0,β2=0.577,β3=1.825,γ1=0.2,γ2=0.8,vd=0.6,μ0=0.7, and initial conditions: x1,2(0)=y1,2(0)=0]

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Figure 23

Bifurcation diagram of α1∊(2.83;3.58) parameter versus x1 displacement for α2=1.093,η1,2,12=0,γ1=0.152,γ2=0.609,vd=0.1,μ0=1.2,β2=1.729,β3=2.441, and initial conditions: τ0=1000,τk=51000,x1(0)=0,x2(0)=0.1,y1,2(0)=0



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